Pair-correlation ansatz for the ground state of interacting bosons in an arbitrary one-dimensional potential

TL;DR

This paper introduces a highly accurate variational ansatz for the ground state of few ultra-cold bosons in one-dimensional traps, capturing correlations across interaction regimes and arbitrary potentials.

Contribution

It presents a novel two-body correlation-based variational scheme that is exact in the noninteracting limit and adaptable to various potential shapes.

Findings

Efficiently describes ground states across interaction strengths.

Accurately encodes boundary conditions for contact interactions.

Reveals limitations of distance-dependent correlations in non-parabolic potentials.

Abstract

We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations have two-body nature. By construction, the proposed ansatz is exact in the noninteracting limit, exactly encodes boundary conditions forced by contact interactions, and gives full control on accuracy in the limit of infinite repulsions. We show its efficiency in a whole range of intermediate interactions for different external potentials. Our results manifest that for generic non-parabolic potentials mutual correlations forced by interactions cannot be captured by distance-dependent functions.